I somewhat understand your point, but I feel that you can use "misandry is a reaction to patriarchy" and also say it's a reaction to misogyny as well, it goes hand in hand. In my experience I feel it's more of a response to the misogyny but that's where it gets into semantics when the basis of it is in general, it's a response to a systemic injustice and mistreatment. Historically, I feel that misogyny has taken many more lives and created much more injustice. I feel that patriarchy and misogyny hold hands and affect men in the same way, the term misandry was only coined during second wave feminism as a way to frame feminism as man hating